SUMMARY

Swifts regularly spend the night flying at high altitude. From previous
studies based on tracking radar observations, we know that they stay airborne
during the night and prefer to orient themselves into the wind direction with
an increased angular concentration with increasing wind speed. In this study,
we investigated the orientation relative to the wind of individual swifts by
frequency (discrete Fourier transform) and autocorrelation analysis based on
time series (10s intervals) of the angle between the swifts' heading and the
wind direction for radar trackings of long duration (9-60 min). The swifts
often showed a significant harmonic oscillation of their heading direction
relative to the wind, with a frequency mostly in the range 1-17 mHz,
corresponding to cycle periods of 1-16 min. The swifts also sometimes
performed circling flights at low wind speeds. Wind speed ranged from 1.3 to
14.8 m s-1, and we expected to find different patterns of
orientation at different wind speeds, assuming that the swifts adapt their
orientation to avoid substantial displacement during their nocturnal flights.
However, oscillatory orientation was found at all wind speeds with variable
frequencies/periods that did not show any consistent relationship with wind
speed. It remains to be shown whether cyclic heading changes are a regular
feature of bird orientation.

Introduction

Common swifts (Apus apus) are remarkable flyers, spending most of
their lives on the wing. Some swifts ascend at dusk and fly during the night
at high altitude until daybreak, when they return to their home colony
(Weitnauer, 1952,
1954,
1960;
Lack, 1956). These nocturnal
flights take place at altitudes up to 3000 m, in more-or-less complete
darkness and often in windy conditions. The nocturnal flight of the swift
requires considerable navigational skills to avoid drifting far away from the
presumed home area. In a previous study
(Bäckman and Alerstam,
2001), we analysed short-duration radar trackings of swifts. We
found that, at higher wind speeds (>9ms-1), the swifts orient
themselves accurately into the wind, but that they are still vulnerable to
being carried away with the wind, e.g. if the wind speed is greater than the
swifts' flight speed. Interestingly, the swifts did not increase their flight
speed to any pronounced degree to avoid displacement. Bruderer and Weitnauer
(1972) suggested that roosting
swifts choose to fly at the minimum power air speed to minimise energy
consumption per unit time. In weak winds, the swifts were less accurate in
orienting themselves towards the wind direction, showing a rather large
scatter around the mean heading direction, which was still oriented into the
wind. Since the trackings we analysed lasted only 30-300s, we could draw no
conclusions about the possible presence of a consistent movement pattern in
swifts flying at low wind speeds
(Bäckman and Alerstam,
2001).

Here, we have chosen a selection of trackings of considerably longer
duration, lasting up to 1 h, to analyse in detail the flight behaviour of
individual roosting swifts. If we assume that the swifts try to remain as
stationary as possible relative to the ground, there will be three different
situations with respect to the wind: (i) the wind speed is higher than the
flight (air) speed of the swift, (ii) the wind speed is approximately equal to
the air speed of the swift and (iii) the wind speed is lower than the air
speed of the swift. We predict that, in situations i and ii, the swifts should
orient consistently into the wind direction, as we observed previously from
the short-duration trackings. The variation in flight direction relative to
the wind should be small, and flight paths relative to the air should be
straight. In case i, we would expect the swifts to drift `backwards'. In case
ii, in contrast, we would expect the drift to be small and in a random
direction. An especially interesting situation emerges in case iii, when the
wind speed is considerably lower than the flight speed of the swift. In this
case, there is a potential risk that the swifts will overshoot their desired
stationary position relative to the ground.

When swifts maintain their mean flight direction into the wind in a weak
wind, as demonstrated in our previous study
(Bäckman and Alerstam,
2001), the risk of displacement could be dealt with in a number of
ways. (i) `Don't care' — maintain the headwind direction without
variation. The swift will overshoot maximally by air speed × time (for
negligible wind speed) and potentially face a return flight in the morning of
the same distance. Usually, there is some wind, and the displacement distance
will then be shorter and the return flight will also take place with a
favourable tail wind. (ii) Circle — in the absence of wind, this will be
the optimal solution. In light winds, the phase of headwind flying should, on
average, be longer than the tailwind phase, with the proportion of time spent
flying into opposing winds increasing with increasing wind speed. (iii) Keep
the average flight direction into the wind and let the instantaneous flight
direction fluctuate around the mean direction, alternately to the left and
right of the headwind course in a more-or-less cyclic way.

In this study, we investigate long nocturnal flights of swifts, as recorded
by tracking radar, to determine the patterns of flight paths and orientation
behaviour at different wind speeds. At high wind speeds, we expect straight
flights relative to the air, with the swifts consistently oriented into the
wind, thus minimising displacement during the night. In contrast, at wind
speeds below the swifts' air speed, we expect more sophisticated strategies of
circling, or oscillating and meandering orientation, effectively neutralising
any long-term resulting movement over the ground.

Materials and methods

We observed swifts Apus apus (L.) in roosting nocturnal flights
using a tracking radar (200kW peak power, 0.25μs pulse duration, 504Hz
pulse repetition frequency, 1.5° beam width, X-band). The radar is
situated on the roof of the Ecology Building in Lund (55°42′N,
13°12′E), 91.5m above sea level. We recorded the flight paths of
swifts during the summer of 1999 between 4 July and 5 August and in the summer
of 2001 between 26 June and 6 July. The radar echoes of swifts are quite easy
to distinguish from those of other birds on the basis of their characteristic
echo signature. Swifts display a typical alternation between wing beating and
longer or shorter gliding intervals. During gliding, the swifts often `tilt'
and make short turns, which appear as rapid changes in the radar echo signal.
The wingbeat frequency of swifts is low enough to be clearly visible on the
radar display, and this, together with the criteria mentioned above, gives the
observer a good indication of whether the target is a swift. Also, in Lund at
this time of the year, we do not expect any other species to use such
flap-gliding flight at night and at high altitude.

For a sample of targets considered to be swifts (N=21), we
recorded and analysed the wingbeat frequency. The wingbeat frequency was
7.0-8.3Hz (mean 7.6Hz), which is in good agreement with earlier recordings for
roosting swifts (Bruderer and Weitnauer,
1972). We tracked only single birds, and our intention was to
track each individual for as long as possible. The radar recorded azimuth,
elevation and range every 2s. The accuracy of radar measurements was limited
to 0.06° in angle (azimuth, elevation) and 10m in range. Wind data were
collected every second hour by releasing and tracking helium balloons.
Azimuth, elevation and range were transferred from the radar to a computer
every 2s by automated data-logging software. Horizontal and vertical positions
were calculated. The position data were averaged from five successive
readings, and the resulting 10s intervals were used to calculate the speed and
track direction (the ground speed vector) of the target. Air speed and heading
direction (the air speed vector) were calculated for each 10s interval by
vector subtraction of the wind velocity at the altitude at which the bird was
flying from its ground speed vector. We used the heading, which is the
directional part of the air speed vector, for further analyses of the swifts'
orientation.

Calculations of mean directions, mean vector lengths (r) and
circular statistics were performed according to Batschelet
(1981). The heading in relation
to the wind (H-W) corresponds to the angular difference between
heading (H) and wind (W) direction; H-W=0° thus
means that the swift is flying straight into the headwind,
H-W=90° that it is heading perpendicular to the wind and
H-W=180° that it is flying in the direction of the tailwind. An
index of straightness (IS) was calculated by dividing the length of
the resulting flight vector by the cumulative sum of the subvectors of each
10s interval. IS is a measure of the straightness of the flight path
and ranges from 0 for a flight with the same start and end positions to 1 for
a perfectly linear flight path. We calculated the index of straightness for
the flight path both relative to the ground (ISg) and
relative to the surrounding air (ISa).

To investigate the flight behaviour in relation to the wind, we focused on
the variations in H-W during a single flight of a swift. To detect
any periodicity in the heading fluctuations relative to the wind direction,
individual H-W data were analysed (i) by autocorrelation for periods
up to n/2, where n is the total number of 10s intervals for
the complete track of an individual swift, and (ii) by frequency analysis,
using the discrete Fourier transform (DFT)
(Chatfield, 1996;
Priestley, 1981). In the DFT
analysis, the H-W data were first `normalised' (residual values from
a linear regression were used) and windowed with the Hanning function. We then
applied a discrete Fourier transform to the data. The resulting power spectrum
was tested for significant (P<0.05) frequency components
(χ2-test of sample spectrum estimator for white noise)
(Jenkins and Watts, 1968). If
there was more than one significant frequency component, we selected the
strongest. We used MATLAB v5.2 (The MathWorks Inc., MA, USA) for all
calculations, and the built-in FFT function for the DFT analysis. As a
control, we applied DFT analysis to 12 long trackings of climbing helium
balloons, using the same criteria as for the analysis of bird trackings, and
found no significant frequency components.

Results

For our analysis, we selected all trackings (N=30) from 1999 with
durations of at least 20 min and up to 60 min. In addition, we selectively
included 19 shorter trackings from 1999 and 2001 of swifts that were flying in
low wind speeds; the duration of these ranged from 9 to 18 min.
Table 1 presents the
characteristics of the swift trackings. The mean flight altitude of our
present sample of 49 swift trackings is very similar to our earlier mean
(altitude 1683±489 m; mean ± S.D.) of a large sample
(N=224) of swift trackings
(Bäckman and Alerstam,
2001). The ground speed varied greatly because of the varying wind
conditions to which the swifts were exposed. The small mean difference between
heading and wind direction shows that the swifts were, on average, well
oriented into the wind direction (Table
1).

Fig. 1 illustrates three
sample tracks. Tracks A and B are from swifts flying in moderate winds (7-8 m
s-1), and track C is from a swift flying in weak winds. In moderate
winds, the swifts often move rather slowly over the ground. The swift in track
A has a net movement towards the wind direction because the air speed of the
swift (9.9 m s-1) is higher than the wind speed (6.9 m
s-1). The resulting ground speed is much lower (3.9 m
s-1). The heading direction of the swift in track A fluctuates
around the headwind direction and causes an undulating movement sideways but,
on average, the difference between the heading and wind direction
(H-W) is only 0.6° and ISa=0.97. The swift in
track B also flies with a mean heading direction almost straight towards the
wind (H-W is on average 9°). In track B, the air speed of the
swift (8.9 m s-1) and the average wind speed (8.1 m s-1)
are very similar. Early in the observed track, the swift shows the same
behaviour as in track A, with H-W fluctuating around zero, but after
approximately 500s the heading direction is on average slightly to the right
of the wind direction; H-W>0. This causes a resulting slow
movement relative to the ground, perpendicularly and to the right of the wind
direction (track B). The ISa is 0.98, revealing a very
consistent orientation into the wind.

Three selected tracks of swifts in nocturnal roosting flight. The blue line
shows the ground track, and the red lines represent the heading direction
every 10s. Numbers denote the time (in s) after the start of tracking. The
arrows beside the letters indicate the wind direction. Geographic north is
upwards. Track A is a swift flying into a wind with a mean direction of
161° and a speed of 6.9 m s-1. The index of straightness
relative to the ground, ISg, is 0.67. In track B, the
swift is facing a wind of 8.1 m s-1 at 314°, and
ISg is 0.59. The corresponding values for track C are 2.9
m s-1, 190° and 0.22.

In track C, the wind speed is only 2.9 m s-1, which is far below
the air speed of the swift (10.2 m s-1). Ground speed is on average
9.6 m s-1. The swift changes its heading continuously and
apparently without consideration of the wind direction. There are several
circling flights, and the ISa is only 0.31. The slightly
higher air speed of this swift may be associated with the fact that it is
descending gently (vertical speed -0.4 m s-1) in contrast to cases
A and B where the swifts fly at almost constant altitude (vertical speeds
+0.15 m s-1 and -0.1 m s-1 respectively).

The index of straightness relative to the ground ISg
does not vary significantly with wind speed
(Fig. 2A). However, we observed
only a small number of swifts flying at wind speeds lower than 5 m
s-1. For the index of straightness relative to the air,
ISa (Fig.
2B), the result is slightly clearer. For wind speeds over 8 m
s-1, the flight paths in relation to the surrounding air are very
straight, but there are a few cases with low ISa values at
lower wind speeds.

Straightness indices in different wind speeds. (A) The straightness index
relative to the ground, ISg. A low value means that the
resulting flight path is greatly convoluted (see
Fig. 1 track C), while a value
close to 1 means that the swift has been flying on a straight course. (B) The
straightness index relative to the surrounding air, ISa.
Circles indicate that the swift has been circling, i.e. that the bird has
crossed its own flight path relative to the ground (ISg)
and the air (ISa).

We were particularly interested in analysing the flight behaviour of the
swifts in relation to the wind direction. In
Fig. 3, we illustrate the time
series (10 s intervals) of H-W over the entire tracking for the same
three trackings as in Fig. 1.
In tracks A and B, the deviations in flight direction from the wind direction
are rather small (within ±50°). In contrast, H-W in track
C fluctuates widely. The largest amplitudes are actually an artefact, since we
are displaying data with a circular distribution on a linear scale
(H-W=+180° is the same as H-W=-180°). In the case of
tracks A and B, this does not matter because the deviations from
H-W=0° are small (H-W is far less than ±180°,
see below), but in case C, where the bird sometimes flies in circles, this way
of analysing course fluctuations becomes inappropriate. Rapid shifts from
H-W=+180° to H-W=-180° should be interpreted as
circling flights.

Analysis of variations in flight direction relative to the wind direction
(H-W) for three selected trackings (same tracks as in
Fig. 1). The first column
presents the deviations from a perfect headwind orientation over the entire
tracking. In the second column, there are autocorrelation diagrams for tracks
A and B. The last column is an alternative analysis of periodicity, in the
form of a DFT power spectrum, showing the relative frequency content of the
H-W data series. Track A has an autocorrelation period of
approximately 160s and a significant frequency component of 6.74 mHz. Track B
shows no distinct period, and the frequency peaks fail to pass the
significance level.

In the second column in Fig.
3, we have analysed the autocorrelation of the H-W values
shown in the first column for tracks A and B. There is an indication of a
cyclic component in the undulating flight path of track A with a period of
approximately 160 s. The corresponding DFT analysis also shows that the
dominant and only statistically significant frequency component is
approximately 7 mHz (seven cycles in 1000 s). In track B, there are no such
clear-cut oscillations of the flight path in the autocorrelation analysis. The
DFT power spectrum shows a number of components, the strongest, but not
significant, component being approximately 2.5 mHz. It is not appropriate to
analyse track C with this method since this swift was flying in circles.

We performed these analyses on all swift tracks where there were no
circling flight paths. The results of the DFT and autocorrelation analyses are
presented in Fig. 4, where we
have divided the values into discrete categories. We found significant
frequency components in 36 trackings and distinct autocorrelation periods in
31 cases, out of 49 trackings. There was no correlation between the wind speed
and the observed distinct autocorrelation periods or between wind speed and
significant frequency components (Fig.
5A,B).

Frequency histogram of the cyclic components of the heading direction
relative to the wind direction (H-W) in our 49 trackings of swifts.
We found a statistically significant frequency component in 36 out of 49
trackings and in 31 trackings with distinct autocorrelation periods.

The periodicity of deviations in the heading direction relative to the wind
direction in relation to wind speed. (A) Significant frequency components
versus wind speed; (B) distinct autocorrelation period
versus wind speed. There was no significant correlation in either
case.

Discussion

The present analysis of long-duration trackings of swifts reveals that the
birds often (but not always) show a pattern of regular variation in their
orientation relative to the wind direction, with a cycle period usually in the
range 1-16 min (corresponding to the frequency range 1-17 mHz; cf.
Fig. 4). The Fourier analysis
also indicated some cases of higher-frequency changes in orientation, at 17-24
mHz (corresponding to a cycle period of 40-60 s). However, contrary to our
expectation, these course variations occurred during flights in both strong
and weak winds (Fig. 5) and
thus in both relatively straight and more meandering flights
(Fig. 2). It is striking that
we often find a regular rhythm in the orientation direction, but there is no
obviously preferred frequency or period. It seems highly unlikely that the
observed patterns are an artefact due to the tracking characteristics of the
radar because the flight paths relative to the ground recorded by radar were
generally very different in degree of convolution as well as in distance
(Table 1) from the flight
paths/heading directions relative to the air on which the frequency analysis
was based.

Because of the time resolution of 10s for the time series, we cannot detect
frequencies higher than 50 mHz, corresponding to a period of 20s. In our set
of data, the shortest period was 40s and the highest frequency was 20 mHz,
which are well within our resolution. Furthermore, it is not possible to
detect frequencies lower than two periods during a flight path. Since the
average tracking duration is 1366s (Table
1), there are few opportunities of finding periods longer than
683s (approximately 11 min), corresponding to a frequency of approximately 1.5
mHz. Still, some very low significant frequencies and long periods emerged
from the analyses of the longest radar trackings in our data set, with the
lowest frequency at 0.3 mHz and the longest period at 25 min. Thus, it is
possible that there exist even slower cyclic patterns than we have described
here.

There seemed to be no consistent relationship between cycle
period/frequency of orientation changes and wind speed
(Fig. 5). This provides no
support for our expectation that swifts might show a regular variation of
their orientation primarily to remain stationary relative to the gound when
flying in rather slow winds. Thus, the possible function of the cyclic
orientation changes during the swifts' flights is unclear. However, we found
that the swifts' flights were sometimes less straight, and occasional circling
occurred, at low wind speeds (Fig.
2), which will contribute to reducing the displacement with
respect to the ground during the night. The cyclic variation in the swifts'
orientation may reflect a behaviour in which the birds do not adjust their
orientation continuously, but rather correct or over-correct it at regular
intervals. However, we found no evidence for any well-defined characteristic
frequency/period for these course corrections. Such behaviour might be
associated with a reduced level of alertness if the swifts are, in some sense,
`sleeping' during their nocturnal flights
(Lack, 1956), or it may be a
phenomenon associated with bird orientation in general.

This is, to our knowledge, the first study in which the existence of
harmonic oscillations in birds' orientation has been investigated and
demonstrated. We have shown that Fourier and autocorrelation analyses provide
useful tools for such investigations of orientation time series. The finding
that swifts flying at night orient into the wind and weave slowly from side to
side by varying their heading into the wind direction with a cycle period of
1-16 min is intriguing. Perhaps this remarkable behaviour is associated with
the swifts' special ability to orient into the wind during the night and at
high altitudes. What is the sensory basis for such behaviour? Is such a
behaviour also involved in the orientation of other birds, for example on
their migratory flights? Unfortunately, these questions cannot be answered
from our existing data, and we have to limit ourselves to proving that
oscillatory orientation occurs in the roosting flights of swifts.

This finding may be of potential importance for understanding the process
of bird orientation. Further analyses of the pattern of variation in
orientation of free-flying birds and of birds in orientation cages are needed
to determine whether such cyclic heading changes should be regarded as a
normal feature of bird orientation or whether they are confined to the special
case of nocturnal roosting flights of swifts orienting into a headwind.

ACKNOWLEDGEMENTS

We are grateful to Björn Holmquist (Department of Statistics, Lund)
and Niklas Jonzén (Department of Theoretical Ecology, Lund) for helpful
suggestions about the analysis of the time series we carried out with the
H-W data. We also thank C.-G. Carlsson and Ulf Olsson at Aerotech
Telub for skilfully installing and adapting the radar, meteorologist Bertil
Larsson for developing efficient software for the treatment of the radar data
and Bertil Ohlsson for improving the English. This study was supported by
grants from the Swedish Natural Science Research Council.